System and method for creating, managing and trading hedge portfolios

ABSTRACT

The present invention discloses apparatuses, systems and methods for providing optimal hedge portfolios that minimize single stock idiosyncratic risk for a given level of transactional costs. This is accomplished by deriving hedge portfolios with the maximum effective n for various levels of transaction costs. In one exemplary embodiment the maximum effective n portfolios are derived by starting with a sample portfolio, such as a capital weighted index, and using a hill climbing algorithm to iteratively modify the sample portfolio to map out the optimal effective n portfolios.

RELATED APPLICATIONS

This application claims priority under 35 USC §119 for U.S. provisionalapplication Ser. No. 60/822,489 filed Aug. 15, 2006. The entire containsof aforementioned application is hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention is generally directed to apparatuses, methods andsystems for investment securities trading. More specifically, thepresent invention discloses systems and methods for the creation ofhedge portfolios to be used to manage risk for actively managedinvestment portfolios.

BACKGROUND OF THE INVENTION

Actively managed investment portfolios often employ hedging strategiesagainst market risk in order to isolate and emphasize the stockselection skill of the portfolio managers. Typically, this isaccomplished by hedging the actively managed portfolio against a capitalweighted index, such as the S&P 500. This practice is based upon theassumption that the selected capital weighted index accurately trackscommon market risk. In other words, the index does not contain anysignificant single stock idiosyncratic risk. Consistent with theseassumptions, the hedge ratio for a particular actively managedinvestment portfolio/capital weighted index combination is determined byperforming a linear regression of the investment portfolio against thecapital weighted index.

SUMMARY OF THE INVENTION

The present invention provides systems, methods and apparatuses fordeveloping optimal hedge portfolios that minimize single stockidiosyncratic risk for a given level of transactional costs. This isaccomplished by deriving hedge portfolios with the maximum effective nfor various levels of transaction costs. In one exemplary embodiment themaximum effective n portfolios are derived by starting with a sampleportfolio, such as a capital weighted index, and using a hill climbingalgorithm to iteratively modify the sample portfolio to map out theoptimal effective n portfolios.

With the optimal hedge portfolio defined for a particular investor, aregression, such as an orthogonal regression, is performed between theinvestor's actively traded portfolio and the optimal hedge. Thisregression is used to determine the appropriate hedge ratio for theinvestor's actively traded portfolio.

An optimal hedge trading system is disclosed to create, trade and managethe optimal hedges disclosed. The system interacts with the investorsand the markets to determine optimal hedge portfolios, match thoseportfolios with the needs of the investor, calculate the appropriatehedge ratio based on the investor's actively traded portfolio, acquirethe optimal hedge portfolio from the markets, and manage and maintainthe optimal hedge portfolio after acquisition.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying appendices and/or drawings illustrate variousnon-limiting, representative, inventive aspects in accordance with thepresent disclosure:

FIG. 1 is a graph demonstrating optimal hedge portfolios in accordancewith an embodiment of the present invention.

FIG. 2 is a flow diagram showing optimal hedge portfolio generation inaccordance with an embodiment of the present invention.

FIGS. 3 a-d are graphs showing regressions in accordance withembodiments of the present invention.

FIG. 4 discloses a optimal hedge generation and trading system inaccordance with one embodiment of the present invention.

FIG. 5 discloses a computer systemization disclosing aspects ofembodiments of the present invention.

The leading number of each reference numeral indicates the first drawingin which that reference numeral is introduced. For example, step 220 isfirst introduced in FIG. 2.

DETAILED DESCRIPTION

Hedges against capital weighted indices do not accurately account forcommon market risk because the indices are subject to price fluctuationsdue to the idiosyncratic behavior of the indices' highly weightedsecurities. Essentially, the largest holdings in the capital weightedindices are a significant enough percentage of the whole thatvariability in highest weighted stocks will move the entire index. Thus,a hedge based on a capital weighted index will not accurately reflectcommon market risks because a significant portion of the index's valuewill be based on the performance of the highly weighted holdings.Accordingly, a hedge based on a capital weighted index will notaccurately represent the investment selection abilities of theinvestment portfolio managers. This problem is most pronounced wheninvestments are concentrated in a particular sector because there is arelatively smaller universe of total stocks and the large entities tendto take up significantly greater portions of the sector index.

The present invention discloses the creation, management and trading ofhedge portfolios that accurately track common market risk and minimizesingle stock idiosyncratic risk relative to trading costs. The level ofstock-specific risks in a portfolio is quantified as the effective n, ñ,of the portfolio. The effective n of a portfolio is defined as thenumber securities in an equal-weighted portfolio with the same level ofstock specific risk as the portfolio being characterized. For example,while the S&P 500 consists of 500 stocks, its effective n might only be115, which would indicate that the S&P 500 is only as diverse as a 115stock equally weighted portfolio. The effective n of a portfolio iscomputed as follows:

${\overset{\sim}{n} = \frac{1}{\sum\limits_{i = 1}^{n}\; w_{i}^{2}}},$where w_(i) equals the weight of each stock in the portfolio and n isthe number of stocks in the portfolio. This leads to a maximum possibleeffective n, ñ, of n, which would represent an equal weighted portfolio.

Equal weighted portfolios minimize single stock idiosyncratic riskbecause each stock contributes equally to the portfolio's performance.Thus, overall portfolio volatility is simply dependent on the number ofsecurities in the portfolio. The volatility of the portfolio decreasesat a rate roughly inverse to the square root of the number of securitiesin the portfolio,

$n,{( \frac{1}{\sqrt{n}} ).}$Thus, an equal weighted hedge portfolio with a high n will provideprotection against volatility due to single stock idiosyncratic risk andtrack common market movements. Large n equal weighted hedge portfolios,however, are expensive due to high trading costs.

The trading costs associated with a given hedge portfolio are the sum ofthe trading costs for the individual securities that make up theportfolio. The trading costs for a given security associated with largeportfolio can be determined based upon a base transactional cost, theaverage percentage change in intra-day price, the average basis pointspread over the life of the purchase order and the size of the orderrelative to the expected market volume over order life. One exemplaryequation for expected trading costs (ETC) is as follows:

${ETC} = {{\beta_{1} + {\beta_{2}\sigma} + {\beta_{3}D} + {\frac{\beta_{4}}{\beta_{5}}\lbrack {( \frac{S}{V^{\gamma}} )^{\beta_{5}} - 1} \rbrack}}:}$where β₁ is a base trading cost; β₂ is a volatility coefficient; σ isthe average percentage intra-day price range; β₃ is coefficient relatingto the size of the order; D is the average basis point spread over thelife of the order; β₄, β₅ and γ are coefficients that relate order sizeto market volume; S is the order size and V is the expected marketvolume over order life.

Trading costs can also be measured as the execution shortfall. For buyorder the execution shortfall can be defined as the execution priceminus the prevailing midquote when the trader received order (strikeprice) as a percentage of strike price, in basis points. For sellorders, execution shortfall is the strike price minus execution price asa percentage of strike price.

A t-cost model, such as the Goldman Sachs U.S. t-cost model, can providepre-trade estimates of an order's execution shortfall. The modelconsists of non-linear regression of execution shortfall on sevenfactors: (1) Order size ($ value); (2) Intra-day execution horizon (e.g.9:30 to 12:30); (3) Market capitalization of stock (large-cap>$7.5billion, mid-cap, small-cap<$1 billion); (4) Listing venue of stock(e.g. NYSE); (5) Average bid-ask quoted spread of stock (in basispoints) over execution horizon; (6) Average trading volume ($) overtrading horizon; (7) Average price volatility of stock (intra-day pricerange % of average price). In one particular embodiment, the model isre-estimated monthly with rolling nine months using a large sample ofactual orders executed over the sample period, such as actual GoldmanSachs all-day and intra-day market orders executed over the sampleperiod. The cost estimates, therefore, reflect how much it actually costto execute similar orders in the past, as opposed to providing a“hypothetical cost” derived using tick data and a theoretical model oftrading. The cost estimates reflect the average trading alpha (orinformation content) of the orders in the estimation sample.

To generate cost estimates using the model the average bid-ask spreads,trading volume, and volatility are used over a daily rolling window ofthe past 21 days. As these averages change over time the cost estimatesreflect these changes. The cost estimates depend on both the executionhorizon and the time-of-day the execution begins, e.g., an order enteredat 9:30 with a two-hour execution horizon will have a different costestimate than the same order with a six-hour horizon because thesix-hour order will interact with a greater volume. Also, because of theintraday volume and bid-ask spread patterns identical two-hour ordersentered at 9:30 and 12:00 will have different trading cost estimates.The model, therefore, can be used to analyze how the size, timing andaggressiveness of an execution influence trading costs. In oneembodiment, the accuracy of the cost model will be determined by thesample data set. For example, if the sample data set has relatively fewintra-day orders above 25% of ADV, estimates will become increasinglyunreliable for order sizes above 25%, likely leading to anunderestimation of the expected cost. In such an embodiment, one mightavoid using the model for order sizes above 50% because it will lacksufficient accuracy.

FIG. 1 is a graph showing the relationship of trading costs to effectiven for different hedge portfolios, for a particular trading sector. The yaxis represents the expected cost of the portfolio as a ratio comparedto the cost of a capital weighted index for that sector. The x axisrepresents the effective n as a ratio compared to n, the total universeof stocks for that sector. The point representing the capital weightedindex for this sector 10 shows that it has an effective n that isapproximately 23% of the effective n of a equal weighted portfolio ofthe stocks in that sector. Point 19 represents the maximum attainableeffective n, which would represent an equally weighted portfolio of allthe stocks in the relevant universe. The expected trading cost of thecapital weighted index 10 is 1.00, which is as expected because thecapital weighted index was used as the benchmark for the cost axis.Optimal hedge portfolio curve 17 represents portfolios with the optimalratio of cost to effective n achievable for this sector. As shown by thehorizontal line leading from point 10 to point 15, point 15 representsthe portfolio having the maximum effective n for the same cost as thecapital weighted index. In this example, an optimal portfolio producedaccording to the disclosed system and with the same transactional costsof the capital weighted index, would have an effective n that isapproximately 49% of the effective n of an equal weighted portfolio ofall the stocks in the sector. This is approximately a two foldimprovement over the effective n of capital weighted index.

As noted above, the points on the optimal hedge portfolio curve 17represent portfolios with optimal effective n for the given tradingcosts. Generating the optimal hedge portfolio curve 17 can beaccomplished in a number of ways. In one embodiment, the transactionalcosts and effective n can be computed for every possible portfoliocombination. This brute force solution will create optimal hedgeportfolio curve 17, but will be relatively computationally expensive.

One optimization of the brute force technique would start with a givenportfolio and then use numerical techniques to optimize the portfolio.For example, by iteratively altering portfolio parameters, such asvarying the securities that make up the portfolio and/or their relativeweights in the portfolio, variations that improve cost or effective ncan be kept and further modified until the optimal portfolio is reachedafter a number of iterations. The iterations continue until you cannotincrease or decrease stock weights without violating the trading costrestriction. Various hill climbing algorithms can accomplish this typeof optimization. Because the problem of solving for the optimaleffective n versus transactional cost portfolio has a global maximum,the optimization will be bounded and a final result will ultimately bereached. In a variation of this embodiment, the optimization routinemight be limited to a certain number of iterations or a certain amountof computation time, which would limit the amount of computationalresources used but may result in an estimate of the true optimal hedgeportfolio curve 17.

Another method for optimizing the generation of the optimal hedgeportfolio curve 17 is to exclude from the universe of eligiblesecurities any securities with excessively expensive trading costs.Certain securities will be expensive to trade because, for example,there is little liquidity or trading volume in the market for thesecurity. Eliminating these hard to borrow, expensive and restrictedsecurities will likely shorten the portfolio generation process it isunlikely that these stocks will be present in the optimal hedgeportfolios at a given cost.

Another technique for optimizing the generation of the optimal hedgecurve is the realization that, for a given portfolio, weights greaterthan

$( \frac{2}{\overset{\sim}{n} + 1} )$for an individual stock increase stock specific risk. Accordingly,reducing the weights of any such stocks in a portfolio should increasethe effective n.

FIG. 2 shows a flow diagram of one exemplary process used to derive theoptimal hedge portfolio curve 17. Variations on this process could bemade by adding or subtracting the optimization techniques discussedabove or by changing the order of the disclosed steps. To begin, theappropriate sector, such as technology or energy, and/or the appropriateinvesting style, such as growth, value, small cap or large cap, isselected 201. A capital weighted index in the relevant sector/style isselected as a starting point 203. Next, the transactional costsassociated with the capital weighted index are computed 205. Theeffective n for the capital weighted index is also computed 207. Inaddition, the universe of securities for the relevant sector/style isdetermined 210 and securities with excessive trading costs are removedfrom the universe 212. In step 220 the capital weighted index ismodified to create a test portfolio with any to the excessive tradingcost securities identified in step 212 removed, other securities fromthe available universe of securities may be added and/or the relativeweight of the securities may be altered, such that the totaltransactional costs of the test portfolio are equal to the transactionalcosts of the capital weighted portfolio. The effective n of the testportfolio is calculated 222. Next, a determination is made whether themax effective n for the given level of transactional costs has beenreached 224. If it has, the optimal hedge portfolio curve 17 has beenreached 230. If not, a determination is made whether the effective n hasincreased 226. If the effective n has increased, this test portfolio iskept 228 and then slightly modified in a return to step 220. If the step226 determination shows that the effective n of the test portfolio hasnot increased, the current test portfolio is discarded and the previoustest portfolio is used 229 as the basis for the next modification andtest iteration in a return to step 220. Over a number of iterations theeffective n of the portfolio will increase until the max effective n forthat cost is reached and step 224 returns a pass to 230. The portfolioproviding the max effective n for that level of transaction costs can berecorded 230.

Other portfolios fitting the optimal hedge portfolio curve 17 can bedetermined by repeating the iterative loop from step 220, but changingthe transactional costs to a different value. For example, reducing thetransactional costs 2% and re-running the iterative loop will output theportfolio at point 16 in FIG. 1. This process can be repeated fordifferent transactional cost to move up and down the optimal hedgeportfolio curve 17.

The above disclosed methods enable the creation of an optimal hedgeportfolio. In a further embodiment, the optimal hedge is used as thebasis for a regression of the investment portfolio to determine a hedgeratio for the optimal hedge investment. As shown in FIG. 3 a, theinvestment portfolio is linearly regressed against the hedge portfolioto create a regression line (R_(Inv))=α₂+β₁(R_(hedge))+error₁. Thepoints on the graph represent the relative returns of the hedgeportfolio and the investment portfolio at particular times. As shown,the linear regression only considers the y axis variance of theinvestment portfolio relative to the hedge portfolio. As shown in FIG. 3b, if a regression were performed such that the hedge was linearlyregressed against the investment portfolio, in would result in aregression line R_(hedge)=α₂+β₂(R_(Inv))+error₂. Simple linearregression is used to calculate hedge ratios based on the assumptionthat β₁=β₂, which is in fact generally not the case. As is shown in FIG.3 c, the regression performed for the investment return against thehedge return is not equal to the regression performed for the hedgereturn against the investment return.

An alternate method of computing hedge ratio, as shown in FIG. 3 d, isto take the symmetric or orthogonal regression (also known as errors invariables regression) of the investment portfolio to the hedgeportfolio. As shown in FIG. 3 d, this method determines the orthogonalvariance of the data points to the line (R_(Inv))=α+β(R_(hedge))+error.This method recognizes that the hedge portfolio is not preciselyequivalent to the market and the regression more accurately reflectsidiosyncratic risk from both the investment portfolio and the hedgeportfolio.

FIG. 4 shows a exemplary embodiment of a trading system implementing themethods previously discussed. In the system an investor 450 creates aninvestment portfolio 460 by trading in one or more investment markets470. The investor consults with the hedge portfolio generation andmanagement processor 480, see FIG. 5 discussion below, to develop anoptimal hedge for the investor's actively traded investment portfolio460. In order to develop the appropriate hedge the composition of theinvestment portfolio 460 is communicated to the hedge portfoliogeneration and management processor 480. The hedge portfolio generationand management processor 480, determines the investment style and/orsector either by examining the investment portfolio or querying theinvestor 450, and uses that information to determine the optimal hedgeportfolio, as discussed above. A regression between the optimal hedgeand the investment portfolio is performed and an appropriate hedge ratiois computed. This process may entail further investor queries todetermine the amount of hedge desired. The hedge portfolio generationand management processor 480 then acquires the securities representingthe hedge through transactions in the investment markets 470. Forexample, the hedge portfolio can be implemented at the stock level viaprogram trade, swap or option combo. The result is the investor's hedgeportfolio 490. The hedge portfolio generation and management processor480 may further perform other beneficial hedge services, such asperiodic rebalancing of the hedge portfolio 490. The operation andmanagement processor may also facilitate corporate actions, theelimination of hard to borrows, moves in/out of industries, and changesin industry classifications.

Hedge Portfolio Generation and Management Controller

FIG. 5 of the present disclosure illustrates inventive aspects of ahedge portfolio generation and management controller 501 in a blockdiagram. In this embodiment, the hedge portfolio generation andmanagement controller 501 may serve to generate manage and trade optimalhedge portfolios.

Typically, users, which may be people and/or other systems, engageinformation technology systems (e.g., commonly computers) to facilitateinformation processing. In turn, computers employ processors to processinformation; such processors are often referred to as central processingunits (CPU). A common form of processor is referred to as amicroprocessor. A computer operating system, which, typically, issoftware executed by CPU on a computer, enables and facilitates users toaccess and operate computer information technology and resources. Commonresources employed in information technology systems include: input andoutput mechanisms through which data may pass into and out of acomputer; memory storage into which data may be saved; and processors bywhich information may be processed. Often information technology systemsare used to collect data for later retrieval, analysis, andmanipulation, commonly, which is facilitated through database software.Information technology systems provide interfaces that allow users toaccess and operate various system components.

In one embodiment, the hedge portfolio generation and managementcontroller 501 may be connected to and/or communicate with entities suchas, but not limited to: one or more users from user input devices 511;peripheral devices 512; and/or a communications network 513.

Networks are commonly thought to comprise the interconnection andinteroperation of clients, servers, and intermediary nodes in a graphtopology. It should be noted that the term “server” as used throughoutthis disclosure refers generally to a computer, other device, software,or combination thereof that processes and responds to the requests ofremote users across a communications network. Servers serve theirinformation to requesting “clients.” The term “client” as used hereinrefers generally to a computer, other device, software, or combinationthereof that is capable of processing and making requests and obtainingand processing any responses from servers across a communicationsnetwork. A computer, other device, software, or combination thereof thatfacilitates, processes information and requests, and/or furthers thepassage of information from a source user to a destination user iscommonly referred to as a “node.” Networks are generally thought tofacilitate the transfer of information from source points todestinations. A node specifically tasked with furthering the passage ofinformation from a source to a destination is commonly called a“router.” There are many forms of networks such as Local Area Networks(LANs), Pico networks, Wide Area Networks (WANs), Wireless Networks(WLANs), etc. For example, the Internet is generally accepted as beingan interconnection of a multitude of networks whereby remote clients andservers may access and interoperate with one another.

The hedge portfolio generation and management controller 501 may bebased on common computer systems that may comprise, but are not limitedto, components such as: a computer systemization 502 connected to memory529.

Computer Systemization

A computer systemization 502 may comprise a clock 530, centralprocessing unit (CPU) 503, a read only memory (ROM) 506, a random accessmemory (RAM) 505, and/or an interface bus 507, and most frequently,although not necessarily, are all interconnected and/or communicatingthrough a system bus 504. Optionally, the computer systemization may beconnected to an internal power source 586. Optionally, a cryptographicprocessor 526 may be connected to the system bus. The system clocktypically has a crystal oscillator and provides a base signal. The clockis typically coupled to the system bus and various clock multipliersthat will increase or decrease the base operating frequency for othercomponents interconnected in the computer systemization. The clock andvarious components in a computer systemization drive signals embodyinginformation throughout the system. Such transmission and reception ofsignals embodying information throughout a computer systemization may becommonly referred to as communications. These communicative signals mayfurther be transmitted, received, and the cause of return and/or replysignal communications beyond the instant computer systemization to:communications networks, input devices, other computer systemizations,peripheral devices, and/or the like. Of course, any of the abovecomponents may be connected directly to one another, connected to theCPU, and/or organized in numerous variations employed as exemplified byvarious computer systems.

The CPU comprises at least one high-speed data processor adequate toexecute program modules for executing user and/or system-generatedrequests. The CPU may be a microprocessor such as AMD's Athlon, Duronand/or Opteron; IBM and/or Motorola's PowerPC; Intel's Celeron, Itanium,Pentium, Xeon, Core and/or XScale; and/or the like processor(s). The CPUinteracts with memory through signal passing through conductive conduitsto execute stored program code according to conventional data processingtechniques. Such signal passing facilitates communication within thehedge portfolio generation and management controller and beyond throughvarious interfaces. Should processing requirements dictate a greateramount speed, parallel, mainframe and/or super-computer architecturesmay similarly be employed. Alternatively, should deployment requirementsdictate greater portability, smaller Personal Digital Assistants (PDAs)may be employed.

Power Source

The power source 586 may be of any standard form for powering smallelectronic circuit board devices such as the following power cells:alkaline, lithium hydride, lithium ion, nickel cadmium, solar cells,and/or the like. Other types of AC or DC power sources may be used aswell. In the case of solar cells, in one embodiment, the case providesan aperture through which the solar cell may capture photonic energy.The power cell 586 is connected to at least one of the interconnectedsubsequent components of the hedge portfolio generation and managementcontroller thereby providing an electric current to all subsequentcomponents. In one example, the power source 586 is connected to thesystem bus component 504. In an alternative embodiment, an outside powersource 586 is provided through a connection across the I/O 508interface. For example, a USB and/or IEEE 1394 connection carries bothdata and power across the connection and is therefore a suitable sourceof power.

Interface Adapters

Interface bus(ses) 507 may accept, connect, and/or communicate to anumber of interface adapters, conventionally although not necessarily inthe form of adapter cards, such as but not limited to: input outputinterfaces (I/O) 508, storage interfaces 509, network interfaces 510,and/or the like. Optionally, cryptographic processor interfaces 527similarly may be connected to the interface bus. The interface busprovides for the communications of interface adapters with one anotheras well as with other components of the computer systemization.Interface adapters are adapted for a compatible interface bus. Interfaceadapters conventionally connect to the interface bus via a slotarchitecture. Conventional slot architectures may be employed, such as,but not limited to: Accelerated Graphics Port (AGP), Card Bus,(Extended) Industry Standard Architecture ((E)ISA), Micro ChannelArchitecture (MCA), NuBus, Peripheral Component Interconnect (Extended)(PCI(X)), PCI Express, Personal Computer Memory Card InternationalAssociation (PCMCIA), and/or the like.

Storage interfaces 509 may accept, communicate, and/or connect to anumber of storage devices such as, but not limited to: storage devices514, removable disc devices, and/or the like. Storage interfaces mayemploy connection protocols such as, but not limited to: (Ultra)(Serial) Advanced Technology Attachment (Packet Interface) ((Ultra)(Serial) ATA(PI)), (Enhanced) Integrated Drive Electronics ((E)IDE),Institute of Electrical and Electronics Engineers (IEEE) 1394, fiberchannel, Small Computer Systems Interface (SCSI), Universal Serial Bus(USB), and/or the like.

Network interfaces 510 may accept, communicate, and/or connect to acommunications network 513. Through a communications network 513, thehedge portfolio generation and management controller is accessiblethrough remote clients 533 b (e.g., computers with web browsers) byusers 533 a. Network interfaces may employ connection protocols such as,but not limited to: direct connect, Ethernet (thick, thin, twisted pair10/100/1000 Base T, and/or the like), Token Ring, wireless connectionsuch as IEEE 802.11a-x, and/or the like. A communications network may beany one and/or the combination of the following: a directinterconnection; the Internet; a Local Area Network (LAN); aMetropolitan Area Network (MAN); an Operating Missions as Nodes on theInternet (OMNI); a secured custom connection; a Wide Area Network (WAN);a wireless network (e.g., employing protocols such as, but not limitedto a Wireless Application Protocol (WAP), I-mode, and/or the like);and/or the like. A network interface may be regarded as a specializedform of an input output interface. Further, multiple network interfaces510 may be used to engage with various communications network types 513.For example, multiple network interfaces may be employed to allow forthe communication over broadcast, multicast, and/or unicast networks.

Input Output interfaces (I/O) 508 may accept, communicate, and/orconnect to user input devices 511, peripheral devices 512, cryptographicprocessor devices 528, and/or the like. I/O may employ connectionprotocols such as, but not limited to: Apple Desktop Bus (ADB); AppleDesktop Connector (ADC); audio: analog, digital, monaural, RCA, stereo,and/or the like; IEEE 1394a-b; infrared; joystick; keyboard; midi;optical; PC AT; PS/2; parallel; radio; serial; USB; video interface:BNC, coaxial, composite, digital, Digital Visual Interface (DVI), RCA,RF antennae, S-Video, VGA, and/or the like; wireless; and/or the like. Acommon output device is a television set, which accepts signals from avideo interface. Also, a video display, which typically comprises aCathode Ray Tube (CRT) or Liquid Crystal Display (LCD) based monitorwith an interface (e.g., DVI circuitry and cable) that accepts signalsfrom a video interface, may be used. The video interface compositesinformation generated by a computer systemization and generates videosignals based on the composited information in a video memory frame.Typically, the video interface provides the composited video informationthrough a video connection interface that accepts a video displayinterface (e.g., an RCA composite video connector accepting an RCAcomposite video cable; a DVI connector accepting a DVI display cable,etc.).

User input devices 511 may be card readers, dongles, finger printreaders, gloves, graphics tablets, joysticks, keyboards, mouse (mice),remote controls, retina readers, trackballs, trackpads, and/or the like.

Peripheral devices 512 may be connected and/or communicate to I/O and/orother facilities of the like such as network interfaces, storageinterfaces, and/or the like. Peripheral devices may be audio devices,cameras, dongles (e.g., for copy protection, ensuring securetransactions with a digital signature, and/or the like), externalprocessors (for added functionality), goggles, microphones, monitors,network interfaces, printers, scanners, storage devices, video devices,video sources, visors, and/or the like.

It should be noted that although user input devices and peripheraldevices may be employed, the hedge portfolio generation and managementcontroller may be embodied as an embedded, dedicated, and/ormonitor-less (i.e., headless) device, wherein access would be providedover a network interface connection.

Memory

Generally, any mechanization and/or embodiment allowing a processor toaffect the storage and/or retrieval of information is regarded as memory529. However, memory is a fungible technology and resource, thus, anynumber of memory embodiments may be employed in lieu of or in concertwith one another. It is to be understood that the hedge portfoliogeneration and management controller and/or a computer systemization mayemploy various forms of memory 529. For example, a computersystemization may be configured wherein the functionality of on-chip CPUmemory (e.g., registers), RAM, ROM, and any other storage devices areprovided by a paper punch tape or paper punch card mechanism; of coursesuch an embodiment would result in an extremely slow rate of operation.In a typical configuration, memory 529 will include ROM 506, RAM 505,and a storage device 514. A storage device 514 may be any conventionalcomputer system storage. Storage devices may include a drum; a (fixedand/or removable) magnetic disk drive; a magneto-optical drive; anoptical drive (i.e., CD ROM/RAM/Recordable (R), ReWritable (RW), DVDR/RW, etc.); and/or other devices of the like. Thus, a computersystemization generally requires and makes use of memory.

Module Collection

The memory 529 may contain a collection of program and/or databasemodules and/or data such as, but not limited to: operating systemmodule(s) 515 (operating system); information server module(s) 516(information server); user interface module(s) 517 (user interface); Webbrowser module(s) 518 (Web browser); database(s) 519; cryptographicserver module(s) 520 (cryptographic server); the hedge portfoliogeneration and management module(s) 535; and/or the like (i.e.,collectively a module collection). These modules may be stored andaccessed from the storage devices and/or from storage devices accessiblethrough an interface bus. Although non-conventional software modulessuch as those in the module collection, typically, are stored in a localstorage device 514, they may also be loaded and/or stored in memory suchas: peripheral devices, RAM, remote storage facilities through acommunications network, ROM, various forms of memory, and/or the like.

Operating System

The operating system module 515 is executable program code facilitatingthe operation of the hedge portfolio generation and managementcontroller. Typically, the operating system facilitates access of I/O,network interfaces, peripheral devices, storage devices, and/or thelike. The operating system may be a highly fault tolerant, scalable, andsecure system such as Apple Macintosh OS X (Server), AT&T Plan 9, Be OS,Linux, Unix, and/or the like operating systems. However, more limitedand/or less secure operating systems also may be employed such as AppleMacintosh OS, Microsoft DOS, Palm OS, Windows2000/2003/3.1/95/98/CE/Millenium/NT/XP (Server), and/or the like. Anoperating system may communicate to and/or with other modules in amodule collection, including itself, and/or the like. Most frequently,the operating system communicates with other program modules, userinterfaces, and/or the like. For example, the operating system maycontain, communicate, generate, obtain, and/or provide program module,system, user, and/or data communications, requests, and/or responses.The operating system, once executed by the CPU, may enable theinteraction with communications networks, data, I/O, peripheral devices,program modules, memory, user input devices, and/or the like. Theoperating system may provide communications protocols that allow thehedge portfolio generation and management controller to communicate withother entities through a communications network 513. Variouscommunication protocols may be used by the hedge portfolio generationand management controller as a subcarrier transport mechanism forinteraction, such as, but not limited to: multicast, TCP/IP, UDP,unicast, and/or the like.

Information Server

An information server module 516 is stored program code that is executedby the CPU. The information server may be a conventional Internetinformation server such as, but not limited to Apache SoftwareFoundation's Apache, Microsoft's Internet Information Server, and/orthe. The information server may allow for the execution of programmodules through facilities such as Active Server Page (ASP), ActiveX,(ANSI) (Objective-) C (++), C2, Common Gateway Interface (CGI) scripts,Java, JavaScript, Practical Extraction Report Language (PERL), Python,WebObjects, and/or the like. The information server may support securecommunications protocols such as, but not limited to, File TransferProtocol (FTP); HyperText Transfer Protocol (HTTP); Secure HypertextTransfer Protocol (HTTPS), Secure Socket Layer (SSL), and/or the like.The information server provides results in the form of Web pages to Webbrowsers, and allows for the manipulated generation of the Web pagesthrough interaction with other program modules. After a Domain NameSystem (DNS) resolution portion of an HTTP request is resolved to aparticular information server, the information server resolves requestsfor information at specified locations on the hedge portfolio generationand management controller based on the remainder of the HTTP request.For example, a request such as http://123.124.125.126/myInformation.htmlmight have the IP portion of the request “123.124.125.126” resolved by aDNS server to an information server at that IP address; that informationserver might in turn further parse the http request for the“/myInformation.html” portion of the request and resolve it to alocation in memory containing the information “myInformation.html.”Additionally, other information serving protocols may be employed acrossvarious ports, e.g., FTP communications across port 21, and/or the like.An information server may communicate to and/or with other modules in amodule collection, including itself, and/or facilities of the like. Mostfrequently, the information server communicates with the hedge portfoliogeneration and management controller, operating systems, other programmodules, user interfaces, Web browsers, and/or the like.

Also, an information server may contain, communicate, generate, obtain,and/or provide program module, system, user, and/or data communications,requests, and/or responses.

User Interface

The function of computer interfaces in some respects is similar toautomobile operation interfaces. Automobile operation interface elementssuch as steering wheels, gearshifts, and speedometers facilitate theaccess, operation, and display of automobile resources, functionality,and status. Computer interaction interface elements such as check boxes,cursors, menus, scrollers, and windows (collectively and commonlyreferred to as widgets) similarly facilitate the access, operation, anddisplay of data and computer hardware and operating system resources,functionality, and status. Operation interfaces are commonly called userinterfaces. Graphical user interfaces (GUIs) such as the Apple MacintoshOperating System's Aqua, Microsoft's Windows XP, or Unix's X-Windowsprovide a baseline and means of accessing and displaying informationgraphically to users.

A user interface module 517 is stored program code that is executed bythe CPU. The user interface may be a conventional graphic user interfaceas provided by, with, and/or atop operating systems and/or operatingenvironments such as Apple Macintosh OS, e.g., Aqua, Microsoft Windows(NT/XP), Unix X Windows (KDE, Gnome, and/or the like), mythTV, and/orthe like. The user interface may allow for the display, execution,interaction, manipulation, and/or operation of program modules and/orsystem facilities through textual and/or graphical facilities. The userinterface provides a facility through which users may affect, interact,and/or operate a computer system. A user interface may communicate toand/or with other modules in a module collection, including itself,and/or facilities of the like. Most frequently, the user interfacecommunicates with operating systems, other program modules, and/or thelike. The user interface may contain, communicate, generate, obtain,and/or provide program module, system, user, and/or data communications,requests, and/or responses.

Web Browser

A Web browser module 518 is stored program code that is executed by theCPU. The Web browser may be a conventional hypertext viewing applicationsuch as Microsoft Internet Explorer or Netscape Navigator. Secure Webbrowsing may be supplied with 128 bit (or greater) encryption by way ofHTTPS, SSL, and/or the like. Some Web browsers allow for the executionof program modules through facilities such as Java, JavaScript, ActiveX,and/or the like. Web browsers and like information access tools may beintegrated into PDAs, cellular telephones, and/or other mobile devices.A Web browser may communicate to and/or with other modules in a modulecollection, including itself, and/or facilities of the like. Mostfrequently, the Web browser communicates with information servers,operating systems, integrated program modules (e.g., plug-ins), and/orthe like; e.g., it may contain, communicate, generate, obtain, and/orprovide program module, system, user, and/or data communications,requests, and/or responses. Of course, in place of a Web browser andinformation server, a combined application may be developed to performsimilar functions of both. The combined application would similarlyaffect the obtaining and the provision of information to users, useragents, and/or the like from the hedge portfolio generation andmanagement controller enabled nodes. The combined application may benugatory on systems employing standard Web browsers.

Hedge Portfolio Generation and Management Controller Module

The hedge portfolio generation and management controller module 535 IsStored program code that is executed by the CPU. The hedge portfoliogeneration and management controller module affects accessing,obtaining, creating, trading, managing, and the provision of optimalhedge portfolios, and/or the like across various communicationsnetworks.

The hedge portfolio generation and management controller module enablingaccess of information between nodes may be developed by employingstandard development tools such as, but not limited to: (ANSI)(Objective-) C (++), Apache modules, binary executables, databaseadapters, Java, JavaScript, mapping tools, procedural and objectoriented development tools, PERL, Python, shell scripts, SQL commands,web application server extensions, WebObjects, and/or the like. Thehedge portfolio generation and management controller module maycommunicate to and/or with other modules in a module collection,including itself, and/or facilities of the like. Most frequently, thehedge portfolio generation and management controller module communicateswith investors, markets, administrators, operating systems, otherprogram modules, and/or the like. The hedge portfolio generation andmanagement controller module may contain, communicate, generate, obtain,and/or provide program module, system, user, and/or data communications,requests, and/or responses.

Distributed Hedge Portfolio Generation and Management Controller

Module

The structure and/or operation of any of the hedge portfolio generationand management controller components may be combined, consolidated,and/or distributed in any number of ways to facilitate developmentand/or deployment. Similarly, the module collection may be combined inany number of ways to facilitate deployment and/or development. Toaccomplish this, one may integrate the components into a common codebase or in a facility that can dynamically load the components on demandin an integrated fashion.

The module collection may be consolidated and/or distributed incountless variations through standard data processing and/or developmenttechniques. Multiple instances of any one of the program modules in theprogram module collection may be instantiated on a single node, and/oracross numerous nodes to improve performance through load-balancingand/or data-processing techniques. Furthermore, single instances mayalso be distributed across multiple controllers and/or storage devices;e.g., databases. All program module instances and controllers working inconcert may do so through standard data processing communicationtechniques.

The configuration of the hedge portfolio generation and managementcontroller will depend on the context of system deployment. Factors suchas, but not limited to, the budget, capacity, location, and/or use ofthe underlying hardware resources may affect deployment requirements andconfiguration. Regardless of if the configuration results in moreconsolidated and/or integrated program modules, results in a moredistributed series of program modules, and/or results in somecombination between a consolidated and distributed configuration, datamay be communicated, obtained, and/or provided. Instances of modulesconsolidated into a common code base from the program module collectionmay communicate, obtain, and/or provide data. This may be accomplishedthrough intra-application data processing communication techniques suchas, but not limited to: data referencing (e.g., pointers), internalmessaging, object instance variable communication, shared memory space,variable passing, and/or the like.

If module collection components are discrete, separate, and/or externalto one another, then communicating, obtaining, and/or providing datawith and/or to other module components may be accomplished throughinter-application data processing communication techniques such as, butnot limited to: Application Program Interfaces (API) informationpassage; (distributed), Component Object Model ((D)COM), (Distributed)Object Linking and Embedding ((D)OLE), and/or the like), Common ObjectRequest Broker Architecture (CORBA), process pipes, shared files, and/orthe like. Messages sent between discrete module components forinter-application communication or within memory spaces of a singularmodule for intra-application communication may be facilitated throughthe creation and parsing of a grammar. A grammar may be developed byusing standard development tools such as lex, yacc, XML, and/or thelike, which allow for grammar generation and parsing functionality,which in turn may form the basis of communication messages within andbetween modules. Again, the configuration will depend upon the contextof system deployment.

The entirety of this disclosure (including the Cover Page, Title,Headings, Field, Background, Summary, Brief Description of the Drawings,Detailed Description, Claims, Abstract, Figures, and otherwise) shows byway of illustration various embodiments in which the claimed inventionsmay be practiced. The advantages and features of the disclosure are of arepresentative sample of embodiments only, and are not exhaustive and/orexclusive. They are presented only to assist in understanding and teachthe claimed principles. It should be understood that they are notrepresentative of all claimed inventions. As such, certain aspects ofthe disclosure have not been discussed herein. That alternateembodiments may not have been presented for a specific portion of theinvention or that further undescribed alternate embodiments may beavailable for a portion is not to be considered a disclaimer of thosealternate embodiments. It will be appreciated that many of thoseundescribed embodiments incorporate the same principles of the inventionand others are equivalent. Thus, it is to be understood that otherembodiments may be utilized and functional, logical, organizational,structural and/or topological modifications may be made withoutdeparting from the scope and/or spirit of the disclosure. As such, allexamples and/or embodiments are deemed to be non-limiting throughoutthis disclosure. Also, no inference should be drawn regarding thoseembodiments discussed herein relative to those not discussed hereinother than it is as such for purposes of reducing space and repetition.For instance, it is to be understood that the logical and/or topologicalstructure of any combination of any program modules (a modulecollection), other components and/or any present feature sets asdescribed in the figures and/or throughout are not limited to a fixedoperating order and/or arrangement, but rather, any disclosed order isexemplary and all equivalents, regardless of order, are contemplated bythe disclosure. Furthermore, it is to be understood that such featuresare not limited to serial execution, but rather, any number of threads,processes, services, servers, and/or the like that may executeasynchronously, concurrently, in parallel, simultaneously,synchronously, and/or the like are contemplated by the disclosure. Assuch, some of these features may be mutually contradictory, in that theycannot be simultaneously present in a single embodiment. Similarly, somefeatures are applicable to one aspect of the invention, and inapplicableto others. In addition, the disclosure includes other inventions notpresently claimed. Applicant reserves all rights in those presentlyunclaimed inventions including the right to claim such inventions, fileadditional applications, continuations, continuations in part,divisions, and/or the like thereof. As such, it should be understoodthat advantages, embodiments, examples, functional, features, logical,organizational, structural, topological, and/or other aspects of thedisclosure are not to be considered limitations on the disclosure asdefined by the claims or limitations on equivalents to the claims.

1. A processor implemented method for providing an optimal hedgeportfolio comprising: receiving an optimal hedge portfolio creationrequest; identifying a relevant investing sector and/or investing style;receiving a requested level of transactional costs determined by theformula${\beta_{1} + {\beta_{2}\sigma} + {\beta_{3}D} + {\frac{\beta_{4}}{\beta_{5}}\lbrack {( \frac{S}{V^{\gamma}} )^{\beta_{5}} - 1} \rbrack}};$deriving via a processor a selection of securities associated with theidentified investing sector and/or investing style representing themaximum achievable effective n for the requested level of transactionalcosts; receiving an investment portfolio; comparing the investmentportfolio to the derived selection of securities to determine a hedgeratio; and processing transactions to determine a hedge portfoliocomprising the derived selection of securities according to the hedgeratio.
 2. The method of claim 1 wherein the optimal hedge ratio isdetermined by performing a regression between the investment portfolioand the hedge portfolio.
 3. The method of claim 2 wherein the regressionis an orthogonal regression.
 4. The method of claim 1 wherein theselection of securities is derived through iteratively processing eachpermeation of portfolio combinations having the requested level oftransaction costs and computing each portfolio combination's effective nto find the maximum.
 5. The method of claim 1 wherein the selection ofsecurities is derived using a hill climbing algorithm.
 6. The method ofclaim 1 wherein the selection of securities is derived by iterativelymodifying and testing portfolio combinations until a maxim effective nis found.
 7. The method of claim 1 wherein the derivation of theselection of securities is limited the maximum effective n for therequested level of transactional costs that can be determined using apre-set amount of time.
 8. The method of claim 1 wherein the derivationof the selection of securities is limited the maximum effective n forthe requested level of transactional costs that can be determined usinga pre-set number of iterations.
 9. The method of claim 1 furthercomprising excluding securities with high transactional costs from theprocess of deriving the selection of securities.
 10. The method of claim1 wherein the derivation of the selection of securities comprisesstarting with a given portfolio and removing securities with weightsgreater than $( \frac{2}{\overset{\sim}{n} + 1} ).$
 11. Themethod of claim 1 wherein the derivation of the selection of securitiescomprises starting with a portfolio of securities held by a capitalweighted index; calculating the transaction costs associated withacquiring the capital weighted index portfolio; and then iterativelymodifying the capital weighted index portfolio to increase the effectiven while maintaining a constant transaction cost.
 12. A processorimplemented method for determining an optimal hedge portfoliocomprising: receiving an investment portfolio to be hedged;characterizing the investment portfolio's relevant sector and/orrelevant investing style; deriving via a processor a hedge portfoliomade up of a collection of securities having a maximum effective n for agiven amount of transaction costs determined by the formula${\beta_{1} + {\beta_{2}\sigma} + {\beta_{3}D} + {\frac{\beta_{4}}{\beta_{5}}\lfloor {( \frac{S}{V^{\gamma}} )^{\beta_{5}} - 1} \rfloor}};$comparing the hedge portfolio to the investment portfolio to determine ahedge ratio.
 13. The method of claim 12 wherein the optimal hedge ratiois determined by performing a regression between the investmentportfolio and the hedge portfolio.
 14. The method of claim 13 whereinthe regression is an orthogonal regression.
 15. The method of claim 12wherein the selection of securities is derived through iterativelyprocessing each permeation of portfolio combinations having therequested level of transaction costs and computing each portfoliocombination's effective n to find the maximum.
 16. The method of claim12 wherein the selection of securities is derived using a hill climbingalgorithm.
 17. The method of claim 12 wherein the selection ofsecurities is derived by iteratively modifying and testing portfoliocombinations until a maxim effective n is found.
 18. The method of claim12 wherein the derivation of the selection of securities is limited themaximum effective n for the requested level of transactional costs thatcan be determined using a pre-set amount of time.
 19. The method ofclaim 12 wherein the derivation of the selection of securities islimited the maximum effective n for the requested level of transactionalcosts that can be determined using a pre-set number of iterations. 20.The method of claim 12 further comprising excluding securities with hightransactional costs from the process of deriving the selection ofsecurities.
 21. The method of claim 12 wherein the derivation of theselection of securities comprises starting with a given portfolio andremoving securities with weights greater than$( \frac{2}{\overset{\sim}{n} + 1} ).$
 22. The method ofclaim 12 wherein the derivation of the selection of securities comprisesstarting with a portfolio of securities held by a capital weightedindex; calculating the transaction costs associated with acquiring thecapital weighted index portfolio; and then iteratively modifying thecapital weighted index portfolio to increase the effective n whilemaintaining a constant transaction cost.
 23. A processor implementedmethod for determining an optimal hedge portfolio comprising: receivingan investment portfolio to be hedged; characterizing the investmentportfolio's relevant sector and/or relevant investing style; derivingvia a processor a hedge portfolio made up of a collection of hedgesecurities and having a maximum effective n for a given amount oftransaction costs determined by the formula${\beta_{1} + {\beta_{2}\sigma} + {\beta_{3}D} + {\frac{\beta_{4}}{\beta_{5}}\lfloor {( \frac{S}{V^{\gamma}} )^{\beta_{5}} - 1} \rfloor}},$wherein the hedge portfolio is determined by starting with a test hedgeportfolio made up of the securities in a capital weighted index andmatched to hedge the investment portfolio's relevant sector and/orrelevant investing style and iteratively modifying the securities in thetest hedge portfolio index using a hill climbing algorithm until amaximum effective n for the given costs is reached; and determining ahedge ratio using an orthogonal regression between the hedge portfolioand the investment portfolio.
 24. A system for providing an optimalhedge portfolio comprising: a memory; a processor disposed incommunication with said memory, and configured to issue a plurality ofprocessing instructions stored in the memory, wherein the processorissues instructions to: receive an optimal hedge portfolio creationrequest; identify a relevant investing sector and/or investing style;receive a requested level of transactional costs determined by theformula${\beta_{1} + {\beta_{2}\sigma} + {\beta_{3}D} + {\frac{\beta_{4}}{\beta_{5}}\lfloor {( \frac{S}{V^{\gamma}} )^{\beta_{5}} - 1} \rfloor}};$and derive a selection of securities associated with the identifiedinvesting sector and/or investing style representing the maximumachievable effective n for the requested level of transactional costs;receive an investment portfolio; compare the investment portfolio to thederived selection of securities to determine a hedge ratio; and acquirea hedge portfolio comprising the derived selection of securitiesaccording to the amounts defined by the hedge ratio.
 25. A system fordetermining an optimal hedge portfolio comprising: a memory; a processordisposed in communication with said memory, and configured to issue aplurality of processing instructions stored in the memory, wherein theprocessor issues instructions to: receive an investment portfolio to behedged; characterize the investment portfolio's relevant sector and/orrelevant investing style; derive a hedge portfolio made up of acollection of securities having a maximum effective n for a given amountof transaction costs determined by the formula${\beta_{1} + {\beta_{2}\sigma} + {\beta_{3}D} + {\frac{\beta_{4}}{\beta_{5}}\lfloor {( \frac{S}{V^{\gamma}} )^{\beta_{5}} - 1} \rfloor}};$and compare the hedge portfolio to the investment portfolio to determinea hedge ratio.